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Massive black holes (BHs) inhabiting galactic nuclei can be described by two parameters only, i.e. mass and spin, that change through cosmic time in response to accretion and merger events. While most numerical simulations accurately track the BH mass, spin evolution is rarely taken into account. In this work, we implement and validate a self-consistent sub-grid model for the evolution of the BH mass and spin via gas accretion in the hydrodynamics code GIZMO. The model assumes that accretion from resolved scales does not occur instantaneously, but is mediated by a sub-grid geometrically thin $α$-disc. After validating our model semi-analytically, we test it in an idealized environment consisting of a circumnuclear disc, where gas accretion onto the accretion disc is consistently determined by GIZMO. In the absence of any accretion-related feedback, the spin evolution closely traces that observed in the semi-analytical models and depends on the free parameters of our implementation, such as the initial BH spin, angular momentum of the accretion disc, and the radius at which the gas inflow circularises. In GIZMO, we also couple our model with the biconical-outflow model presented in a companion paper, wherein the feedback axis is always aligned with the BH spin. In this last case, the evolution of the central BH differs significantly from the previous cases, since the feedback process modifies the gas dynamics and its inflow rates from resolved scales. Such an interaction cannot be modeled by simple semi-analytical models and should be treated using full N-body hydrodynamical simulations.